Region-based quantitative and hierarchical attribute reduction in the two-category decision theoretic rough set model

•An improved type of classification regions and its preservation reduct are proposed.•The set-region preservation target, property and reduct are studied.•The double-preservation reduct of set regions and rule consistency is established.•Hierarchies of three quantitative reducts and two qualitative reducts are explored.

Quantitative attribute reduction exhibits applicability but complexity when compared to qualitative reduction. According to the two-category decision theoretic rough set model, this paper mainly investigates quantitative reducts and their hierarchies (with qualitative reducts) from a regional perspective. (1) An improved type of classification regions is proposed, and its preservation reduct (CRP-Reduct) is studied. (2) Reduction targets and preservation properties of set regions are analyzed, and the set-region preservation reduct (SRP-Reduct) is studied. (3) Separability of set regions and rule consistency is verified, and the quantitative and qualitative double-preservation reduct (DP-Reduct) is established. (4) Hierarchies of CRP-Reduct, SRP-Reduct, and DP-Reduct are explored with two qualitative reducts: the Pawlak-Reduct and knowledge-preservation reduct (KP-Reduct). (5) Finally, verification experiments are provided. CRP-Reduct, SRP-Reduct, and DP-Reduct expand layer by layer Pawlak-Reduct and exhibit quantitative applicability, and the experimental results indicate their effectiveness and hierarchies regarding Pawlak-Reduct and KP-Reduct.